Tlusty has six goals and 10 points in 37 games this season.
To replace him on the roster the Hurricanes recalled forward Zach Boychuk from Charlotte of the American Hockey League.
Boychuk had an assist in his only NHL game this season, a 5-3 Carolina victory against the San Jose Sharks on Dec. 6.
Boychuk leads Charlotte in goals (14) and points (27) and is first in the AHL with 10 power-play goals and tied for first with 16 power-play points. He's been on a tear of late with 12 goals in his past 16 AHL games.
I don't have a crystal ball. Predicting is a real complicated thing. If we stay healthy, have enough depth and get the good goaltending we think we're going to have, you can go all the way. But a lot of things have to happen. There's going to be a lot of teams that think the same thing. Everyone made deals. We're all are optimistic about where we'll end up.
— Rangers general manager Glen Sather after being asked if he's constructed a team that can win the Stanley Cup before their 4-1 win against the Predators on Monday